Although he is referred to as 'Megamouth' (and sometimes Jaws) in the game files and on the stats.txt file in the Spelunky directory folder, he is known as 'Old Bitey' in the HD version.
However, his obvious resemblance to the shoal of ordinary Piranha he swims with leads most to think of him as 'Giant Piranha'.

This giant fish is the one enemy in the Jungle that you don't want to fight without being prepared. In fact, you might not even know it exists, due to a combination of the moderate chance of the flooded cavern level appearing, and that you will usually never have to go into the water to complete the level.

Simply reaching Megamouth is an ordeal in itself - the water it resides in is filled with swarms of the smaller Piranha, which might kill you long before Megamouth decides to chase you. The boss does drop four supply crates, which tend to carry ropes and bombs, but you may always get lucky and find something very useful.

The Piranha is virtually impossible to whip without taking heavy amounts of damage. The best way to kill it is to use a Gun - of which the Shotgun is preferred due to the higher damage output, ease of aiming and ability to hit lots of the smaller Piranha at once.
Remember that Megamouth needs to be hit by at least ten bullets (each buckshot fires 6 pellets) before dying and tends to be bodyblocked by the large number of Piranha around him.
Slapping a Sticky Bomb onto him is guaranteed to get the job done if you want to risk getting close enough to do it.

There is a method for relatively safely defeating a Giant Piranha with just your whip, using no other items. It can be safe and reliable for expert players.
First, clear out a screen's worth of piranhas, as you'll need an empty area to work. This is the riskiest part, so be careful not to take damage from the piranhas.
Second, lure Megamouth to you and get above or beneath him (best done by hopping out of the water for a moment which causes him to freeze). Position your self above or below the exact center of his width (about where his red pectoral fin ends) and he will spin in place helplessly.
From there, swim up or down INTO his body (only his head will hurt you) and whip furiously. This method is extremely reliable when perfected, but may take a few failures at first to learn.

curious fact, he dosent appears as an skeleton like the normal piranhas in an restless dead flooded cavern level